Angular velocity sensor having cantilever beams

ABSTRACT

An angular velocity sensor comprises a substrate, a vibrating member of an elongate plate formed by processing a part of the substrate, a support beam formed by processing a part of the substrate to support a center of the vibrating member in a longitudinal direction thereof, a driving device for driving both longitudinal ends of the vibrating member to vibrate in a first direction, and a detecting device for detecting vibrations of the vibrating member in a second direction perpendicular to the first direction thereby to detect an angular velocity of rotation of the substrate.

This application is a continuation of application Ser. No. 07/985,157,filed Dec. 3, 1992, now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an angular velocity sensor fordetecting an angular velocity by utilizing occurrence of a Coriolisforce corresponding to the angular velocity of rotation of a vibrator ina direction perpendicular to a vibrating direction of the vibrator whenthe vibrating vibrator is rotated.

2. Related Background Art

Since a mechanical rotating top rate gyroscope is large and expensive,there has been developed an angular velocity sensor for public use ascalled as a piezoelectric gyroscope or oscillation gyroscope which iseffective in power savings, longer in life, and suitable for decrease insize.

FIG. 1 is a perspective view to show a conventional angular velocitysensor comprising such an oscillation gyroscope. A vibration piece fordetection 4 is mounted through a coupling member 3 above a vibrationpiece 2 fixed on a base 1, while a vibration piece for detection 7 ismounted through a coupling member 6 above a vibration piece 5 similarly.There are provided on the vibration piece 2 a piezoelectric elementdrive 8 vibrating the vibration piece 2 in the X-direction and apiezoelectric element for monitor 9 for monitoring actual vibrations ofthe vibration piece 2. Also, a piezoelectric element detector 10 isprovided on the vibration piece for detection 4 to detect vibrations inthe Y-direction. Similarly, a piezoelectric element drive 11 and apiezoelectric element monitor 12 are provided on the vibration piece 5,and a piezoelectric element detector 13 is on the vibration piece fordetection 7.

In the above arrangement, while the vibration pieces 2, 5 are vibratingat a resonance frequency ω1 with a constant amplitude as opposing toeach other in the X-direction, and when the vibration pieces 2, 5 arerotated together with the base 1 at an angular velocity Ω about theZ-axis, a Coriolis force Fc proportional to the angular velocity Ω actson the vibration pieces for detection 4, 7 to vibrate the vibrationpieces for detection 4, 7 at the resonance frequency ω1. Since anamplitude of the vibrations of the vibration pieces for detection 4, 7is proportional to the angular velocity Ω, the angular velocity Ω may beobtained by detecting the amplitude of the vibrations by thepiezoelectric elements for detection 10, 13. In the detection, in orderto keep the amplitude of the vibration pieces 2, 5 constant, theamplitude is detected by the piezoelectric elements monitor 9, 12 andthe detected amplitude is fed back to each drive signal of thepiezoelectric element drives 8, 11.

The above-described conventional example, However, includes a drawbackof an inability of increase in detection precision of angular velocitybecause the resonance frequency would be deviated and the attenuationproperty would be distributed unless the work and assembly precision ofthe vibration pieces 2, 5 and the vibration pieces for detection 4, 7should be high. In addition, since the parts are not integrally made,the assembly becomes complicated and the sensor cannot be made smalleror cheaper.

An angular velocity sensor free of the above drawbacks was proposed inJapanese Laid-open Patent Application No. 61-139719. FIG. 2 is anexploded perspective view to show a construction of the angular velocitysensor as disclosed. In FIG. 2, reference numeral 51 designates asubstrate made of silicon, 52 a spacer, and 53 a support substrate madeof silicon. A cantilever beam 50 is formed on the substrate 51 byetching. An electrode 54 is provided at a free end of the cantileverbeam 50. An AC signal is applied from a generator 55 to the electrode 54to vibrate the free end of the cantilever beam 50 in the Z-direction.

In FIG. 2, when the substrate 51 rotates about the Y-axis, the free endof the cantilever 50 is vibrated by a Coriolis force in the X-direction.Since an amplitude of the vibrations in the X-direction corresponds toan angular velocity of rotation, the angular velocity may be measured bydetecting the vibrations by piezo resistance elements 56a and 56bmounted on the cantilever beam.

There appears, however, a force to vibrate the fixed end as a reactionto the vibrations at the free end in the arrangement of FIG. 2. Thisforce is absorbed by a material of the substrate, and, therefore, thevibrations of the free end are attenuated by an amount as absorbed.Thus, the angular velocity sensor of FIG. 2 is not effective to generatethe vibrations in the Z-direction, and has a loss in vibrations in theX-direction, resulting in a decrease in detectivity.

SUMMARY OF THE INVENTION

It is an object of the present invention to solve the above problems inthe conventional sensors and to provide an angular velocity sensor whichcan be efficiently driven while having a high detectivity.

The object of the present invention can be achieved by an angularvelocity sensor comprising a substrate, a vibrating member of anelongate plate formed by processing a part of the substrate, a supportbeam formed by processing a part of the substrate to support a center ofthe vibrating member in a longitudinal direction thereof, driving meansfor driving both longitudinal ends of the vibrating member to vibrate infirst direction, and detecting means for detecting vibrations of thevibrating member in a second direction perpendicular to the firstdirection thereby to detect an angular velocity of rotation of thesubstrate.

The object of the invention can also be achieved by an angular velocitysensor comprising a substrate, a first cantilever beam formed byprocessing a part of the substrate and having a fixed end and avibrating end supported capable of vibrating relative to the fixed end,a second cantilever beam formed by processing a part of the substrateand having a fixed end and a vibrating end supported capable ofvibrating relative to the fixed end, the first and second cantileverbeams being formed in symmetry with each other with a symmetry axisbeing on a fixed end side thereof, driving means for driving thevibrating ends of the first and second cantilevers to vibrate in a firstdirection, and detecting means for detecting vibrations of the first andsecond cantilever beams in a second direction perpendicular to the firstdirection thereby to detect an angular velocity of rotation of thesubstrate.

Since the angular velocity sensor according to the present invention isstructured such that the both ends of the vibrator are vibrated and thevibrator is supported at the center thereof, forces generated by thereaction to the vibrations at both ends are balanced to cancel eachother at the center to cause no loss of vibrations in the supportportion. Therefore, the angular velocity sensor according to the presentinvention may efficiently generate vibrations while increasing thedetectivity of angular velocity.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic perspective view to show a first example of aconventional angular velocity sensor;

FIG. 2 is a schematic perspective view to show a second example of aconventional angular velocity sensor;

FIG. 3 is an exploded perspective view to show a first embodiment of anangular velocity sensor according to the present invention;

FIG. 4 is a schematic sectional view of the angular velocity sensor asshown in FIG. 3;

FIG. 5 is a block diagram to show drive and detection circuits of theangular velocity sensor as shown in FIG. 3;

FIG. 6 is an exploded perspective view to show a second embodiment ofthe angular velocity sensor according to the present invention; and

FIG. 7 is a schematic sectional view of the angular velocity sensor asshown in FIG. 6.

FIG. 8 is a perspective view showing a third embodiment of the angularvelocity sensor according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be explained in detail in accordance withembodiments as shown in FIG. 3 to FIG. 8.

FIG. 3 is an exploded perspective view to show a first embodiment of theangular velocity sensor according to the present invention. In FIG. 3, avibrator 22 and a support beam 23 are integrally formed on a vibratorsubstrate 21 made of a semiconductor substrate such as silicon by thephotolithography and the anisotropic etching. The vibrator 22 comprisestwo sections 22a and 22b, and the central portion thereof is supportedby the support beam 23. Coils for drive 24a and 24b are formed on eitherend portion of the vibrator 22 by photolithography patterning, which areled along above the support beam 23 to terminals 25. A diffused typestrain gauge unit is formed in the central portion of the vibrator 22 bydoping the silicon substrate with an impurity such as boron. In thestrain gauge unit, a plurality of strain gauges 26a to 26d areincorporated in a bridge form to detect a strain as a change in voltage.There is a detection circuit 27 also formed on the vibrator substrate 21in the monolithic manner similarly by the photolithography, which is fortemperature compensation of the strain gauges 26a to 26d and forarithmetic operations of respective outputs.

A support substrate 28 made of a semiconductor substrate such as siliconis disposed below the vibrator substrate 21, which has in the centralportion thereof a support base 29 formed by the anisotropic etching.Further, a plate permanent magnet 30 made of a ferrite or a rare earthmagnet is disposed at the lowermost position to provide a magnetic fieldnormally through the vibrator substrate 21. The vibrator substrate 21and the support substrate 28 are assembled by the anode couplingprocess, in which the substrates 21, 28 are pressed toward each other ata high temperature of about 400° C. and a high voltage is appliedthereto. Then, the permanent magnet 30 and the support substrate 28 areglued to each other with an adhesive.

FIG. 4 is a sectional view of the angular velocity sensor of FIG. 3 inthe assembled state. In FIG. 4, the central portion of the vibrator 22is fixed on the support base 29, and the both ends thereof, on which thecoils for drive 24a and 24b are disposed, can be freely vibrated.

In the above arrangement, when an excitation current is supplied to eachof the coils for drive 24a and 24b, the vibrator 22 is repelled orattracted by a magnetic field of the permanent magnet 30 to vibrate in aprimary vibration direction perpendicular to a surface of the vibratorsubstrate 21. The excitation currents are set to coincide with theresonance frequency of the vibrator 22, and directions of the currentsflowing through the coils for drive 24a, 24b are arranged to move bothends of the vibrator 22 in the same phase in the Z-direction.Additionally, outputs of the strain gauges 26a to 26d are fed back tothe excitation currents to keep an amplitude of the vibrator 22 alwaysconstant. In detail, in case that the vibrator 22 is vibrating only inthe Z-direction, an output obtained by summing the outputs of the straingauges 26a, 26b is of the same phase and proportional to a deflectionamount of the vibrator to provide an amplitude of Z-direction. In casethat the vibrator 22 is vibrating not only in the Z-direction but alsoin the X-direction, the X-directional vibrations cause one of the straingauges 26a, 26b to expand but the other to contract, providingrespective strains in opposite phase with the same amplitude. When thestrains are added, the X-directional vibrations cancel each other andonly the Z-directional amplitude is output. A certain amplitude may bekept by feedback of the Z-directional amplitude to the amplitudes of theexcitation currents of the coils for drive 24a, 24b. The same is truefor the strain gauges 26c, 26d on the other side, in which control ismade to keep the amplitude constant.

If an angular velocity Ω of rotation about the Y-axis is applied ontothe sensor in that state from the outside, a Coriolis force Fc works ina direction perpendicular to the vibration direction of the vibrator 22,that is, in the X-direction. Then, the vibrator 22 vibrates in theX-direction with an amplitude proportional to the angular velocity Ω ofrotation acting on the vibrator vibrating at the resonance frequency. Adifference is obtained between outputs of the strain gauges 26a, 26b toremove the same phase components caused by the Z-directional vibrationsand extract only outputs of opposite phase components caused by theX-directional vibrations in detection of the X-directional vibrations ofthe vibrator 22. The difference between the outputs of the strain gauges26a, 26b is equivalent to an amplitude of the X-directional vibrations.Since the amplitude is proportional to the angular velocity of rotationΩ, the angular velocity of rotation Ω may be detected in the sensor. Theabove is also the case for the strain gauges 26c, 26d. In order to gainan angular velocity for rotation Ω, detection is necessary for takingout an amplitude from the X-directional vibrations amplitude-modulated.The Z-directional vibration signal and the X-directional vibrationsignal of the vibrator 22 is synchronously detected to detect theangular velocity of rotation Ω.

FIG. 5 is a block diagram to show an example of constitution of drivecircuits and detection circuits in the first embodiment of the angularvelocity sensor according to the present invention. In FIG. 5, the samemembers are given the same numerals as in FIG. 2. In FIG. 5, analternating current is supplied from an AC power source 40a throughterminals 25 to a coil for drive 24a to vibrate one portion 22a of avibrator 22. Also, an alternating current is supplied from an AC powersource 40b through terminals 25 to a coil for drive 24b to vibrate theother portion 22b of the vibrator 22.

Each of strain gauges 26a and 26b mounted on the portion 22a of thevibrator 22 outputs a signal in which a periodic signal corresponding tothe X-directional vibrations and a periodic signal corresponding to theZ-directional vibrations are superposed on each other, as describedabove. The signals from the strain gauges 26a, 26b are transmitted to adifferential amplifier 42a in the detection circuit 27, in which adifference is taken between the signals. The differential amplifier 42aoutputs a periodic signal corresponding to the X-directional vibrations.The X-directional vibrations are caused by a Coriolis force in rotationof the substrate 21. Accordingly, an angular velocity detection signalmay be obtained by effecting synchronous detection of an amplitude ofthe output signal of the differential amplifier 42a by use of aZ-directional vibration signal described latter as a reference signal bya first amplitude detector 44a.

A summing amplifier 43a in the detection circuit 27 obtains a sum of theoutput signals of the strain gauges 26a and 26b to output a periodicsignal corresponding to the Z-directional vibrations. The Z-directionalvibrations are caused by the coil for drive 24a. Thus, a control signalmay be obtained by detecting an amplitude of the output signal of thesumming amplifier 43a by a second amplitude detector 45a. The controlsignal is fed back to the driving means to control an amplitude of thecurrent supplied from the AC power source 40a through an amplitudecontrol circuit 41a to the coil 24a, whereby the portion 22a of thevibrator may be stably vibrated with a constant amplitude.

The same detection as described is carried out with outputs of straingauges 26c and 26d mounted on the portion 22b of the vibrator.Specifically, a differential amplifier 42b takes a difference between heoutputs of the strain gauges 26c and 26d, and an angular velocitydetection signal is obtained by synchronously detecting an amplitude ofan output signal of the differential amplifier 42b by use of theZ-directional vibration signal as a reference signal by a thirdamplitude detector 44b. Also, a summing amplifier 43b takes a sum of theoutputs of the strain gauges 26c and 26d, and a control signal isobtained by detecting an amplitude of an output signal of the summingamplifier 43b by a fourth amplitude detector 45b. An output signal ofthe fourth amplitude detector 45b is fed back to an amplitude controlcircuit 41b to control an amplitude of the output current of the ACpower source 40b. The outputs of the first and the third amplitudedetectors 44a and 44b can be individually used as respective angularvelocity detection signals, or, an adder 46 can serve to add them toprovide an output as an angular velocity detection signal as shown inFIG. 5.

Although the coils 24a and 24b are driven by the separate AC powersources 40a and 40b in the above embodiment, they may be driven by acommon power source in an alternative arrangement. In the alternativearrangement, the outputs of the second and the fourth amplitudedetectors 45a and 45b are added, and an amplitude of an output currentof the common power source is controlled based on the sum signal.

In the present embodiment, when the portions 22a and 22b of the vibrator22 are vibrated, forces caused by reaction to the vibrations becomebalanced in the portion of the support beam 23 against each other tocause no loss in vibrations. Thus, the portions 22a and 22b may beefficiently driven and the dissipation power of the driving means may beminimized. Further, the X-directional vibrations due to the Coriolisforce are not damped, so that the angular velocity may be detected witha high detectivity. In addition, since a moment acting on the supportbase 29 which serves as the fixed ends of the portion 22a and 22b can bemade smaller than that in a case of a cantilever and a load working onthe connecting portion to the support base 29 can be also made small,the durability of the sensor may be improved.

FIG. 6 is an exploded perspective view to show a second embodiment ofthe angular velocity sensor according to the present invention, and FIG.7 is a sectional view of the angular velocity sensor of FIG. 6 in anassembled state. In the second embodiment, a piezoelectric element drive31 is substituted for the coils for drive 24a and 24b to vibrate thevibrator 22. The production of the piezoelectric element 31 is asfollows: A lower electrode 34 is formed on the substrate 33 bypatterning; A piezoelectric layer 35 such as PZT, ZnO, and Al₃ N₄ isthen deposited thereon; An upper electrode 36 and an extractionelectrode 37 are formed by patterning; and the piezoelectric layer 35 isfinally removed excluding the piezoelectric element drive 31 and theperiphery thereof. A pattern of outgoing lines from the electrode 34 aresimultaneously formed. An extraction electrode 38 is provided at aposition corresponding to the upper electrode 36 on the back plane ofthe vibrator substrate 21 to connect between the upper electrode 36 andthe extraction electrode 37 when coupled with the piezoelectric layer35.

In the present embodiment, an amplitude voltage is applied to thepiezoelectric element drive 31 also serving as a support base to vibratethe vibrator 22. The excitation voltage is controlled at the resonancefrequency of the vibrator 22 to keep the amplitude of the vibrator 22constant based on sum signals of the strain gauges 26a to 26d similarlyas in the first embodiment. The use of the piezoelectric element 31allows the permanent magnet 30 to be omitted and the sensor to be madecompact.

Further, a great number of very small sensors may be simultaneouslyproduced in production by the micromechanics, permitting a greatreduction in production cost.

In the present embodiment, the detection of the angular velocity iscarried out in the same manner as in the first embodiment and the sameeffect may be enjoyed. Additionally in the present embodiment, a singlepiezoelectric element provided on the central portion of the vibrator isused to vibrate both ends of the vibrator, so that the angular velocitysensor obtained may be simple in structure and may be operatedefficiently.

FIG. 8 is a perspective view to show an arrangement of vibrators of athird embodiment. Vibrators 22, 22' parallelly arranged by thephotolithography and the anisotropic etching are integrally formed on avibrator substrate 21 made of a semiconductor substrate such as siliconsuch that the central portions of the vibrators are supported by asupport beam 23. A driving coil not illustrated is provided on each ofend portions 22a, 22b, 22a' 22b' of the vibrators 22, 22', in the samemanner as in the first embodiment. The vibration driving is performed bythe driving coils such that the amplitude of the vibration becomesconstant in a Z-direction perpendicular to the surface of the vibratorsubstrate 21. In this moment, the both end portions 22a, 22b of thevibrator 22 move in the Z-direction with the same phase while both endportions 22a', 22b' of the vibrator 22' move opposite to that of the endportions 22a, 22b with the same phase. Such the movement of the endportions 22a', 22b', 22a , 22b can be realized by adjusting thedirections of currents flowing in the driving coils provided on the endportions of the vibrators 22, 22'. Further, strain gauges notillustrated are provided in the vicinity of the support beam 23 of therespective vibrators 22, 22', in the same manner as the firstembodiment, so that the vibration of the vibrators 22, 22' in theX-direction can be detected.

When an angular velocity Ω of rotation about the Y-axis is applied fromthe outside, Coriolis forces Fc work on the end portions 22a, 22b, 22a',22b' of the vibrators 22, 22' in directions indicated by the arrows inFIG. 8 according to the respective excitation direction in theZ-direction, so that both end portions 22a, 22b of the vibrator 22 andboth end portions 22a', 22b' of the vibrator 22' phase oppositelyvibrate in the X-direction each other with an amplitude proportional tothe angular velocity Ω of rotation. The Z-directional vibration signaland the X-directional vibration signal are detected by the strain gaugesnot illustrated of the vibrators 22, 22' and the X-directional vibrationsignal and the Z-directional vibration signal are synchronously detectedto detect the angular velocity of rotation in the same manner as thefirst embodiment.

Since reaction forces against the Coriolis forces Fc occured on thevibrators 22, 22' in the X-direction due to the angular velocity Ω ofrotation become balanced through the support beam 23 of the portionbetween the vibrators 22, 22' by arranging the vibrators 22, 22'parallelly each other, there can be provided an angular velocity sensoraccording to the third embodiment in which an energy loss of vibrationcan be minimized and an angular velocity of rotation can be detectedwith high sensitivity.

Further, a load working on the connecting portion to a supporting base,not illustrated, for fixing the support beam 23 can be made small, sothat the durability of the angular velocity sensor can be improved.

The present invention may be applicable to many widely differentembodiments in addition to the embodiments as described above. Forexample, a piezoelectric element may be used as means for detectingvibrations of the vibrator. It should be understood that the presentinvention includes all such embodiments and modifications withoutdeparting from the scope of the appended claims.

What is claimed is:
 1. An angular velocity sensor comprising:asubstrate; a vibrating member of an elongate plate formed on part ofsaid substrate and extending in a longitudinal direction along a firstaxis, said vibrating member having first and second longitudinal endsextending from a central portion in opposite directions along the firstaxis; a support beam whose longitudinal axis extends along a second axisperpendicular to the longitudinal direction of said vibrating member,said support beam being formed on part of said substrate to support saidvibrating member at said central portion along the second axis betweensaid first and second longitudinal ends of said vibrating member;driving means for driving both of said longitudinal ends of saidvibrating member to vibrate in a first direction perpendicular to asurface of said substrate; and detecting means for detecting vibrationsof said vibrating member in a second direction perpendicular to saidfirst direction to detect an angular velocity of rotation of saidsubstrate, wherein said first and second longitudinal ends of saidvibrating member are positioned opposite to each other with respect tosaid support beam.
 2. An angular velocity sensor according to claim 1,wherein said driving means comprises first and second coils provided onsaid first and second longitudinal ends of said vibrating member, apermanent magnet applying a magnetic field to said first and secondcoils, and a power source for supplying an alternating current to saidfirst and second coils.
 3. An angular velocity sensor according to claim1, wherein said driving means comprises a piezoelectric element providedat a center of said vibrating member in the longitudinal directionthereof.
 4. An angular velocity sensor according to claim 1, whereinsaid detecting means comprises a first strain gauge unit formed on oneside of said vibrating member with respect to a center thereof, a secondstrain gauge unit formed on the other side of said vibrating member withrespect to the center, and a detection circuit for detecting anamplitude of the vibrations of said vibrating member from outputs ofsaid first and second strain gauge units.
 5. An angular velocity sensoraccording to claim 4, wherein said substrate is a semiconductor and partof said substrate is doped with an impurity to provide said first andsecond strain gauge units.
 6. An angular velocity sensor according toclaim 5, wherein said detection circuit is formed in a part of saidsubstrate in a monolithic manner.
 7. An angular velocity sensoraccording to claim 4, wherein said first strain gauge unit comprisesfirst and second strain gauges formed on said vibrating member asjuxtaposed in the second direction, wherein said second strain gaugeunit comprises third and fourth strain gauges formed on said vibratingmember as juxtaposed in the second direction, and wherein said detectioncircuit comprises a first differential circuit for obtaining adifference between outputs of said first and second strain gauges, afirst amplitude detector for detecting an amplitude of an output signalof said first differential circuit, a first summing circuit forobtaining a sum of outputs of said first and second strain gauges, asecond amplitude detector for detecting an amplitude of an output signalof said first summing circuit, a first feedback circuit for conductingfeedback of an output signal of said second amplitude detector to saiddriving means, a second differential circuit for obtaining a differencebetween outputs of said third and fourth strain gauges, a thirdamplitude detector for detecting an amplitude of an output signal ofsaid second differential circuit, a second summing circuit for obtaininga sum of the outputs of said third and fourth strain gauges, a fourthamplitude detector for detecting an amplitude of an output signal ofsaid second summing circuit, and a second feedback circuit forconducting feedback of an output signal of said fourth amplitudedetector to said driving means.
 8. An angular velocity sensor accordingto claim 1, wherein said substrate is a semiconductor and said vibratingmember and said support beam are etched on said substrate.
 9. An angularvelocity sensor comprising:a substrate:a first cantilever beam formed onpart of said substrate and having a first fixed end and a firstcantilevered vibrating end; a second cantilever beam formed on part ofsaid substrate and having a second fixed end and a second cantileveredvibrating end, said first and second cantilever beams formed to besymmetrical with each other and having a central portion at said fixedends, wherein a longitudinal direction of said first cantilever beam isoriented along a first axis and in the same direction as a longitudinaldirection of said second cantilever beam, wherein the first and secondcantilevered vibrating ends are on opposite ends from each other in thelongitudinal directions of said first and second cantilever beams; asupport beam whose longitudinal axis extends along a second axisperpendicular to the longitudinal directions of said first and secondcantilever beams, said support beam supporting the first and secondfixed ends at said central portion along the second axis between thefirst and second fixed ends; driving means for driving said vibratingends of said first and second cantilever beams to vibrate in a firstdirection perpendicular to a surface of said substrate; and detectingmeans for detecting vibrations of said first and second cantilever beamsin a second direction perpendicular to the first direction to detect anangular velocity of rotation of said substrate.
 10. An angular velocitysensor according to claim 9, wherein said driving means comprises firstand second coils provided on said vibrating ends of said first andsecond cantilever beams, respectively, a permanent magnet for applying amagnetic field to said first and second coils, and a power source forsupplying an alternating current to said first and second coils.
 11. Anangular velocity sensor according to claim 9, wherein said driving meanscomprises a piezoelectric element mounted midway between said first andthe second cantilever beams.
 12. An angular velocity sensor according toclaim 9, wherein said detecting means comprises a first strain gaugeunit formed on said first cantilever beam, a second strain gauge unitformed on said second cantilever beam, and a detection circuit fordetecting an amplitude of the vibrations of said first and secondcantilever beams from outputs of said first and second strain gaugeunits.
 13. An angular velocity sensor according to claim 12, whereinsaid substrate is a semiconductor and part of said substrate is dopedwith an impurity to provide said first and second strain gauge units.14. An angular velocity sensor according to claim 13, wherein saiddetection circuit is formed in a part of said substrate in a monolithicmanner.
 15. An angular velocity sensor according to claim 12, whereinsaid first strain gauge unit comprises first and second strain gaugesformed on said first cantilever beam as juxtaposed in the seconddirection, and said second strain gauge unit comprises third and fourthstrain gauges formed on said second cantilever beam as juxtaposed in thesecond direction, and wherein said detection circuit comprises a firstdifferential circuit for obtaining a difference between outputs of saidfirst and second strain gauges, a first amplitude detector for detectingan amplitude of an output signal of said first differential circuit, afirst summing circuit for obtaining a sum of the outputs of said firstand second strain gauges, a second amplitude detector for detecting anamplitude of an output signal of said first summing circuit, a firstfeedback circuit for conducting feedback of an output signal of saidsecond amplitude detector to said driving means, a second differentialcircuit for obtaining a difference between outputs of said third andfourth strain gauges, a third amplitude detector for detecting anamplitude of an output signal of said second differential circuit, asecond summing circuit for obtaining a sum of the outputs of said thirdand fourth strain gauges, a fourth amplitude detector for detecting anamplitude of an output signal of said second summing circuit, and asecond feedback circuit for conducting feedback of an output signal ofsaid fourth amplitude detector to said driving means.
 16. An angularvelocity sensor according to claim 9, wherein said substrate is asemiconductor and wherein said first and second cantilever beams areetched on said substrate.